Spectroscopy and radiative transfer are rapidly growing fields within atmospheric and planetary science with implications for weather, climate, biogeochemical cycles, air quality on Earth, as well as the physics and evolution of planetary atmospheres in our solar system and beyond. Remote sensing and modeling atmospheric composition of the Earth, of other planets in our solar system, or of planets orbiting other stars require detailed knowledge of how radiation and matter interact in planetary atmospheres. This includes knowledge of how stellar or thermal radiation propagates through atmospheres, how that propagation affects radiative forcing of climate, how atmospheric pollutants and greenhouse gases produce unique spectroscopic signatures, how the properties of atmospheres may be quantitatively measured, and how those measurements relate to physical properties. This book provides this fundamental knowledge to a depth that will leave a student with the background to become capable of performing quantitative research on atmospheres. The book is intended for graduate students or for advanced undergraduates. It spans across principles through applications, with sufficient background for students without prior experience in either spectroscopy or radiative transfer. Courses based on this book are intended to be accompanied by the development of increasing sophisticated atmospheric and spectroscopic modeling capability (ideally, the student develops a computer model for simulation of atmospheric spectra from microwave through ultraviolet).